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Nilpotent connections and the monodromy theorem: Applications of a result of turrittinPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 39
(x)) in K 0 (Y ) by Proposition 5.1. Furthermore, using the projection formula
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The difference F * (θ p (Ω) −1 ) − 1 is contained in Num 0 (f ) if and only if, for all x ∈ K 0 (X), the Adams-Riemann-Roch formula ψ p (f * (x)) = f * (θ p (Ω) −1 · ψ p (x)) in K 0 (Y )
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follows from the projective space bundle theorem (see Theorem 2.3 on p
From Corollary 4.10 it now follows as in Theorem (6.2) in [Ko5] that this formula holds already in K q (G, Y ) if l is a prime with l | ord(G) and Y is a Z
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Let G be a subgroup of G and Y a noetherian scheme. In section 6 in [Ko5], we have raised the following question: Under which conditions does the induction formula ψ l
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Mapping a locally free module on a scheme to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this paper, we prove some formulas of Riemann-Roch type for the behavior of this tensor power operation with respect to the push-forward homomorphism associated with a projective morphism between schemes. We furthermore establish analogous formulas for higher K-groups.
Mathematische Zeitschrift – Springer Journals
Published: Apr 1, 2000
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